We have developed a method to calculate relative binding free energies for several (5-10) ligands binding to the same protein from a single computer simulation. Our chemical-Monte Carlo/Molecular Dynamics calculations have been applied to study a family of nonnucleoside inhibitors of HIV reverse transcriptase (HIV-RT), and yielded free energies in good agreement with experiment. The facilities of the Computer Graphics Laboratory was used to monitor the progress of the simulations, and to prepare an image from one of our calculations which was used as the signature graphic for "Docking and Scoring: Molecular Recognition in Drug Design", a Molecular Design Institute conference.